An x-Coordinate Point Compression Method for Elliptic Curves over Fp

• Published in: 2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing pp. 65 - 71
• Main Authors: Dudeanu, A, Oancea, George-Razvan, Iftene, S
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.09.2010
• Subjects: compact representation; Complexity theory; Compression algorithms; cube roots; cubic equations; Elliptic curve cryptography; Elliptic curves; Polynomials
• ISBN: 9781424498161; 1424498163
• DOI: 10.1109/SYNASC.2010.23

In this paper we propose an x-coordinate point compression method for elliptic curves over F p , where p >; 3 is prime, as an alternative to the classical y-coordinate point compression method. A point P̃ = (x̃, y) will be compressed as P = (x, y) where x has only two bits and, thus, our method allows more compact representations when [log 2 x] >; [log 2 y]+1. Both our compression and decompression algorithms involve solving cubic equations or, in some cases, only computing cube roots modulo a prime, thus being of worst-case complexity O((log 2 p) 4 ). For some particular cases, our compression algorithm can be significantly improved, requiring only two multiplications (thus, being of worst-case complexity O((log 2 p) 2 )).